two.grp.fixed.a0 {BayesPPD}

Model fitting for two groups (treatment and control group, no covariates) with fixed a0

Description

Model fitting using power priors for two groups (treatment and control group, no covariates) with fixed a_0

Usage

two.grp.fixed.a0(
  data.type,
  y.c,
  n.c,
  v.c,
  historical = matrix(0, 1, 4),
  prior.mu.c.shape1 = 1,
  prior.mu.c.shape2 = 1,
  nMC = 10000,
  nBI = 250
)

Arguments

data.type

Character string specifying the type of response. The options are "Normal", "Bernoulli", "Poisson" and "Exponential".

y.c

Sum of responses for the control group.

n.c

Sample size of the control group.

v.c

(For normal data only) sample variance of responses for the control group.

historical

(Optional) matrix of historical dataset(s). If data.type is "Normal", historical is a matrix with four columns:

• The first column contains the sum of responses for the control group.

• The second column contains the sample size of the control group.

• The third column contains the sample variance of responses for the control group.

• The fourth column contains the discounting parameter value a_0 (between 0 and 1).

For all other data types, historical is a matrix with three columns:

• The first column contains the sum of responses for the control group.

• The second column contains the sample size of the control group.

• The third column contains the discounting parameter value a_0 (between 0 and 1).

Each row represents a historical dataset.

prior.mu.c.shape1

First hyperparameter of the initial prior for \mu_c. The default is 1. Does not apply if data.type is "Normal".

prior.mu.c.shape2

Second hyperparameter of the initial prior for \mu_c. The default is 1. Does not apply if data.type is "Normal".

nMC

(For normal data only) number of iterations (excluding burn-in samples) for the Gibbs sampler. The default is 10,000.

nBI

(For normal data only) number of burn-in samples for the Gibbs sampler. The default is 250.

Details

The power prior is applied on the data of the control group only. Therefore, only summaries of the responses of the control group need to be entered.

If data.type is "Bernoulli", "Poisson" or "Exponential", a single response from the treatment group is assumed to follow Bern(\mu_t), Pois(\mu_t) or Exp(rate=\mu_t), respectively, where \mu_t is the mean of responses for the treatment group. The distributional assumptions for the control group data are analogous.

If data.type is "Bernoulli", the initial prior for \mu_t is beta(prior.mu.t.shape1, prior.mu.t.shape2). If data.type is "Poisson", the initial prior for \mu_t is Gamma(prior.mu.t.shape1, rate=prior.mu.t.shape2). If data.type is "Exponential", the initial prior for \mu_t is Gamma(prior.mu.t.shape1, rate=prior.mu.t.shape2). The initial priors used for the control group data are analogous.

If data.type is "Normal", the responses are assumed to follow N(\mu_c, \tau^{-1}) where \mu_c is the mean of responses for the control group and \tau is the precision parameter. Each historical dataset D_{0k} is assumed to have a different precision parameter \tau_k. The initial prior for \tau is the Jeffery's prior, \tau^{-1}, and the initial prior for \tau_k is \tau_k^{-1}. The initial prior for the \mu_c is the uniform improper prior. Posterior samples are obtained through Gibbs sampling.

Value

The function returns a S3 object with a summary method. If data.type is "Normal", posterior samples of \mu_c, \tau and \tau_k's (if historical data is given) are returned in the list item named posterior.params. For all other data types, two scalars, c_1 and c_2, are returned in the list item named posterior.params, representing the two parameters of the posterior distribution of \mu_c. For Bernoulli responses, the posterior distribution of \mu_c is beta(c_1, c_2). For Poisson responses, the posterior distribution of \mu_c is Gamma(c_1, c_2) where c_2 is the rate parameter. For exponential responses, the posterior distribution of \mu_c is Gamma(c_1, c_2) where c_2 is the rate parameter.

References

Chen, Ming-Hui, et al. "Bayesian design of noninferiority trials for medical devices using historical data." Biometrics 67.3 (2011): 1163-1170.

See Also

power.two.grp.fixed.a0

Examples

data.type <- "Bernoulli"
y.c <- 70
n.c <- 100

# Simulate three historical datasets
historical <- matrix(0, ncol=3, nrow=3)
historical[1,] <- c(70, 100, 0.3)
historical[2,] <- c(60, 100, 0.5)
historical[3,] <- c(50, 100, 0.7)

set.seed(1)
result <- two.grp.fixed.a0(data.type=data.type, y.c=y.c, n.c=n.c, historical=historical)
summary(result)